Sounds interesting - Do you have a link for that, or if you've got time could you explain?
TL;DR: if you compress CO2 to above 73 bar, it becomes supercritical fluid, which has a density almost like water and which does not mix with water. If we inject this fluid into underground saline aquifers, we can trap it indefinitely. Basically exactly the reverse of producing oil and gas. In this case you're transporting and injecting pure CO2, not water with 0.1% - 1% CO2.
It's been done at large scale since the mid-1990s, so we know it's viable. Lots of research and development on details/optimization still to be done, but we know it will work and we know we can scale it up.
Just because the CO2 concentration is so much higher in exhaust/flue gas, 10-40% versus 0.04% in the atmosphere, it's much more cost effective in the next 50-ish years.
In many cases, aquifers are so huge that injecting even a few million tonnes of CO2 makes only a small difference in pressure. And if the pressure did increase too much, we would drill a well deep at the aquifer bottom and take out some of the water.